Question 38520
 Let f= 1 2 3 4 5 
       2 3 1 5 4  

and 
  
g= 1 2 3 4 5 
   3 4 2 5 1.

What is f inverse -1?
 
 {{{f^-1 }}} 
 = (1 2 3 4 5)
   (3 1 2 5 4)
               
Write fog as a product of disjoint cycles.Is fog even?why?
 if you define fog (x) = f(g(x)) then
 fog = 
 (1 2 3 4 5)
 (1 5 3 4 2) 
 as disjoint cycles, it is
 (2 ,5) 
 one transpoition, hence it is odd.

 You have to work hard.
 
 Kenny